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I'm trying to translate the following:

[...] quem autem valorem aliter nisi appropinquando cognoscere non datur.

Which comes from Euler (De Serie Lambertina/e). But I'm having trouble sorting out what's what. A literal translation might be

[...] which value however otherwise even if knowing to be approached is not given.

The issue I'm having is the combined use of a gerundive (or gerund), appropinquando ('to be approached, ought to be approached') with the infinite cognoscere ('to know, knowing, to be familiar with') followed by a passive verb, datur ('to be given'). All this is in a clause using both 'nisi...' ('even if, if not') and non. To make matters more confusing for me, 'quem valorem' seems like it could be used in an indirect statement with cognoscere, but then I don't know what the dative or ablative gerund and the passive verb are referring to, or how to translate it anyway.

How does this construction work, and how is the sentence translated idiomatically to English?

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The main verb of the clause, datur is impersonal. In English the subject 'it' would be used (though, grammatically speaking, the real subject is the infinitive cognoscere).
→ '...it isn't given/granted/permitted...' or even '...it isn't possible....'

Remember that cognoscere really means 'know' or to 'be familiar with' only in the perfective tenses (perfect, pluperfect, future perfect). In the imperfective tenses, it means 'to learn,' to become familiar with,' 'to find out,' or the like. Again, cognoscere is the subject of the passive verb datur, the thing that isn't possible.
→ '...it isn't possible to learn....'

Quem valorem supplies the direct object of cognoscere. There's no indirect statement. To translate quem, you may want to treat it as a connecting relative – that is, equavelent to et or sed + the appropriate form of a demonstrative (e.g., hunc or eum).
→ '...but it isn't possible to learn this value...' (more literally, '...which value it isn't possible to learn...').

The adverb aliter modifies cognoscere and means 'in another way' or, as we may say, 'in any other way.'
→ '...but it isn't possible to learn this value in any other way....'

The conjunction nisi, in addition to 'if not' and 'unless,' also means 'unless' or 'except'. (I don't think it ever means 'even if.') Here, it introduces the second term in the comparison started by aliter.
→ '...but it isn't possible to learn this value in any other way except....'

Appropinquando isn't a passive infinitive, as you've translated it; so it doesn't mean 'to be approached.' Rather, it's the gerund, which is active in meaning. Here, it's in the ablative (ablative of means) and answers to aliter by providing the only other way that it's possible to learn the value. (Note that it can't be a gerundive, because a gerundive is an adjective; but there's nothing in the ablative for it to modify here.)
→ '...but it isn't possible to learn this value in any other way except by approximating it.'

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  • In Comments to Mitomino's answer to Q: latin.stackexchange.com/q/10679/1982, the point was made that a gerundive, in the oblique cases, loses both its deontic & passive qualities, effectively becoming a gerund. Two examples from Pinkster's: (i) "patriam ipsam inflammandam reliquimus." (Cic. Fam. 16.12.1) = "We abandoned our mother-city to (the) burning."; (ii) "placet contra gaudere nosmet omittendis doloribus." (Cic. Fin. 1.56) = "but on the other hand to celebrate by (the) releasing the pains.".
    – tony
    Commented Feb 26, 2021 at 13:17
  • The only benefit to using a gerundive, in the oblique cases, is the agreement of case endings. Therefore, the gerundive, in this context, becomes a gerund (active; verbal noun) while retaining agreement in number, case & gender. Do you agree with this?
    – tony
    Commented Feb 26, 2021 at 13:28
  • @tony, I don't agree that it 'becomes' a gerund. Clearly, though, it has long been well-established something like omittendis doloribus is equivalent, in terms of sense, to omittendo dolores (gerund + direct object). I think something quite different is going on in the patriam ipsam inflammandam example, where the gerundive is predicative. I, for one, wouldn't say that the gerundive is equivalent to a gerund even in terms of sense in that instance; then again, I have no particular background in linguistics, nor have I read the comments that you refer to.
    – cnread
    Commented Feb 26, 2021 at 17:42
  • Thank you. In example (i) pinkster may have mistranslated: "We abandoned our mother-city to burning." To burning what, the bread? In English we would use either a gerund ("...to the burning.") or an infinitive ("...to burn."). If a gerund works in English, why not in Latin? This would give gerundive, "inflammandam", behaving as a gerund while requiring the agreement of case-ending, number & gender.
    – tony
    Commented Feb 28, 2021 at 9:20
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I'd put it this way:

"[...] which value however cannot be known other than by approximation [I think this is the mathematical term]."

'Literally' (I don't like that term and don't really think it makes sense, but anyhow):

"[...] which value however other than by approximation ('by approaching', a gerund in the ablative) to know (it) is not given."

datur = 'it is given' ('to be given' would be dari, the present passive infinitive).

Does that help you? :-)

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  • Thanks a lot! I'm still trying to wrap my head around the sentence, but having a valid translation makes it much easier. Would you say 'cognoscere non datur' is taken as one part (so to speak)? Something like "knowing cannot be taken [for granted]"? And is this a common form?
    – Sam Gallagher
    Commented Feb 24, 2021 at 18:23
  • The writer below is right, 'cognoscere' is the subject of 'datur', "to learn (it) is not given," i.e. it cannot be learned, i.e. it cannot be known. (All this is a bit academic, in my humble view.)
    – Batavulus
    Commented Feb 24, 2021 at 18:40

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